Анизотропные жидкости. Биологические структуры. Петрова Г.П. - 11 стр.

    ?keb ϑ = π 2 i_ji_g^bdmeyjgh_ jZkiheh`_gb_  lh Q = −1 2 .
LZd dZd n = −n  lh ^ey nmgdpbb f kijZ\_^eb\h f (ϑ ) = f (π − ϑ ) .
    IZjZf_lju ihjy^dZ fh]ml [ulv hij_^_e_gu dZd
                  cosϑ = ( an ) = ∫ f (ϑ ) cosϑ d ω ≡ 0 P1 ,

            Q=
                 1
                 2
                   (                 )   1
                                                    (
                   3cos2 ϑ − 1 = ∫ f (ϑ ) 3cos2 ϑ − 1
                                         2
                                                                )dω =   P2 .   (2 )

< h[s_f kemqZ_ fh`gh aZibkZlv
                            Q = Pl = ∫ f (ϑ ) Pl (cosϑ )dω ,                      (3 )

]^_ O — q_lgh_ qbkeh LZdbf h[jZahf nmgdpby hjb_glZpbhggh]h
jZkij_^_e_gby fhe_dme g_fZlbq_kdhc nZau fh`_l [ulv ij_^klZ\
e_gZ k mq_lhf \deZ^h\ ke_^mxsbo fmevlbihe_c dhlhju_ aZibku
\Zxlky \ \b^_ ihebghfh\ E_`Zg^jZ
                                          ∞
                            f (ϑ ) = ∑ Cl Pl (cosϑ ) ,
                                         l =0
ijb wlhf dhwnnbpb_glu Cl fh]ml [ulv ij_^klZ\e_gu \ \b^_
                        Cl = ( 2l + 1) 2 Pl ( cosϑ ) .
< h[s_f kemqZ_ ^ey dhwnnbpb_glh\ J fhf_glh\ jZkij_^_e_gby
kijZ\_^eb\Z nhjfmeZ
                            
                                 (              )
                                         n
                        d n  cos 2 ϑ − 1 
                    1
               Pn = n                     , n = 0, n! = 1 .
                   2 n!        ( dω )n

< qZklghklb
     P0 = 1, P1 = cosϑ , P2 =
                              3cos 2 ϑ − 1
                                   2
                                                 1
                                                        (
                                           , P3 = 5cos3 ϑ − 3cosϑ ≡ 0 ,
                                                 2
                                                                           )
                           1
                             {
                      P4 = 35cos 4 ϑ − 30cos 2 ϑ + 3 ,
                           8
                                                            }
>ey nmgdpbb hjb_glZpbhggh]h jZkij_^_e_gby bf__f
                              2l + 1
                   f (ϑ ) = ∑        Pl Pl (cosϑ ) ,
                                2    l
]^_ Pl = ∫ Pl (cosϑ ) f (ϑ )sinϑ dϑ — iZjZf_lj g_fZlbq_kdh]h hjb_g
lZpbhggh]h ihjy^dZ
    Ke_^mxsb_ aZ 3 kdZeyjgu_ iZjZf_lju ihjy^dZ mqblu\Zxl
                        

fhe_dmeyjgu_ nemdlmZpbb \ kj_^_ ba l\_j^uo kl_j`g_c
    < g_dhlhjuo nbabq_kdbo wdki_jbf_glZo gZijbf_j ijb bamq_
gbb nemhj_kp_gpbb beb dhf[bgZpbhggh]h jZkk_ygby \ `b^dbo
djbklZeeZo m^Z_lky hij_^_eblv g_ lhevdh P2 = Q  gh b P4 .
10